Optimization of a high gain observer for feedback linearization control

Abstract

In this paper, a continuous–discrete time observer using an optimized high gain is proposed for a robotic manipulator where the output is time sampled. The main contribution of this approach is to improve the value of the high gain that corresponds to the minimum value of the cost function by using some metaheuristic algorithms. The observer is characterized by an optimal high gain that is optimized by biogeography-based optimization (BBO) algorithm, particle swarm optimization (PSO) method and genetic algorithms (GA). Through this investigation, it is proven that the best optimization results are obtained through the process based on the BBO algorithm. BBO is a relatively new nature-inspired optimization algorithm used to find the best and optimal value for an optimization problem. The introduced method is implemented in two steps. In the first step the high gain is optimized in an off-line way by the BBO algorithm. In the second step, the obtained optimal value is inserted on-line in a feedback control loop. The suggested optimized observer is used for two purposes: first it ensures an accurate estimation of state variables that are not physically measurable; despite the presence of disturbances and measurement noises; second it guarantees a stability of the considered system and the convergence of the estimation error. Results of simulated experimentations for robot manipulators are presented in order to demonstrate the performance and effectiveness of the proposed observer optimization.

Keywords

• Biogeography based optimization
• Continuous-discrete time observers
• High gain observers
• Particle swarm optimization
• Robotic manipulators